Note that this value is about an order of magnitude larger than the one predicted to be accessible in the head-on collision of state-of-the-art petawatt-class high-intensity-laser and free-electron-laser (FEL) pulses of \(\omega \simeq {\cal O}(10)\,{\rm keV}\)  [1]}, [2]}.
At the same time, for the present parameters the fraction of incident gamma photons scattered into a perpendicularly polarized mode is given by \(N_\perp /N\simeq 2.53\times 10^{-10}\) .
For x-rays of \(\omega \simeq {\cal O}(10)\,{\rm keV}\)  the possibility of measuring such tiny ellipticities has been demonstrated experimentally [3]}, [4]}, [5]}.
However, we emphasize that these techniques developed for x-ray polarimetry can certainly not be used at \(400\,{\rm MeV}\) . In the latter parameter regime rather pair-production polarimetry may be an option [6]}, [7]}, but the possibility to measure tiny ellipticities such as the one in Eq. (REF ) with this technique remains to be shown.
For proposals of prospective experimental schemes to measure high-energy vacuum birefringence utilizing pair production in matter to determine the polarization state of the outgoing probe photons, cf. Refs. [8]}, [9]}, [10]}, [11]}.
